Properties

Label 6027.2.a.bn.1.13
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(0\)
Dimension: \(24\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.368135 q^{2} -1.00000 q^{3} -1.86448 q^{4} +0.572097 q^{5} -0.368135 q^{6} -1.42265 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.368135 q^{2} -1.00000 q^{3} -1.86448 q^{4} +0.572097 q^{5} -0.368135 q^{6} -1.42265 q^{8} +1.00000 q^{9} +0.210609 q^{10} +5.73282 q^{11} +1.86448 q^{12} +3.53946 q^{13} -0.572097 q^{15} +3.20522 q^{16} +1.83305 q^{17} +0.368135 q^{18} +5.95881 q^{19} -1.06666 q^{20} +2.11045 q^{22} +3.12066 q^{23} +1.42265 q^{24} -4.67270 q^{25} +1.30300 q^{26} -1.00000 q^{27} -0.0143419 q^{29} -0.210609 q^{30} -6.00517 q^{31} +4.02526 q^{32} -5.73282 q^{33} +0.674809 q^{34} -1.86448 q^{36} +7.68699 q^{37} +2.19365 q^{38} -3.53946 q^{39} -0.813895 q^{40} +1.00000 q^{41} +6.01972 q^{43} -10.6887 q^{44} +0.572097 q^{45} +1.14883 q^{46} +6.07970 q^{47} -3.20522 q^{48} -1.72019 q^{50} -1.83305 q^{51} -6.59925 q^{52} -0.555156 q^{53} -0.368135 q^{54} +3.27973 q^{55} -5.95881 q^{57} -0.00527975 q^{58} +7.46748 q^{59} +1.06666 q^{60} -10.8150 q^{61} -2.21072 q^{62} -4.92861 q^{64} +2.02492 q^{65} -2.11045 q^{66} +3.12025 q^{67} -3.41767 q^{68} -3.12066 q^{69} -8.70596 q^{71} -1.42265 q^{72} +8.02113 q^{73} +2.82985 q^{74} +4.67270 q^{75} -11.1101 q^{76} -1.30300 q^{78} +5.75556 q^{79} +1.83370 q^{80} +1.00000 q^{81} +0.368135 q^{82} -13.4857 q^{83} +1.04868 q^{85} +2.21607 q^{86} +0.0143419 q^{87} -8.15579 q^{88} -2.84026 q^{89} +0.210609 q^{90} -5.81840 q^{92} +6.00517 q^{93} +2.23815 q^{94} +3.40902 q^{95} -4.02526 q^{96} -17.0640 q^{97} +5.73282 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} - 24q^{3} + 32q^{4} - 4q^{5} - 8q^{6} + 24q^{8} + 24q^{9} + O(q^{10}) \) \( 24q + 8q^{2} - 24q^{3} + 32q^{4} - 4q^{5} - 8q^{6} + 24q^{8} + 24q^{9} + 4q^{10} + 12q^{11} - 32q^{12} + 4q^{15} + 44q^{16} - 8q^{17} + 8q^{18} + 4q^{19} - 28q^{20} + 16q^{22} + 20q^{23} - 24q^{24} + 48q^{25} - 32q^{26} - 24q^{27} + 24q^{29} - 4q^{30} + 4q^{31} + 36q^{32} - 12q^{33} - 16q^{34} + 32q^{36} + 64q^{37} - 20q^{38} + 48q^{40} + 24q^{41} + 20q^{43} + 48q^{44} - 4q^{45} + 28q^{46} - 32q^{47} - 44q^{48} - 20q^{50} + 8q^{51} + 76q^{53} - 8q^{54} + 24q^{55} - 4q^{57} + 28q^{58} - 28q^{59} + 28q^{60} + 28q^{61} + 4q^{62} + 48q^{64} + 28q^{65} - 16q^{66} + 44q^{67} + 32q^{68} - 20q^{69} + 20q^{71} + 24q^{72} + 16q^{73} + 44q^{74} - 48q^{75} + 16q^{76} + 32q^{78} + 4q^{79} - 44q^{80} + 24q^{81} + 8q^{82} - 8q^{83} + 28q^{85} + 56q^{86} - 24q^{87} + 60q^{88} - 60q^{89} + 4q^{90} + 60q^{92} - 4q^{93} - 24q^{94} + 28q^{95} - 36q^{96} + 48q^{97} + 12q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.368135 0.260311 0.130155 0.991494i \(-0.458452\pi\)
0.130155 + 0.991494i \(0.458452\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.86448 −0.932238
\(5\) 0.572097 0.255850 0.127925 0.991784i \(-0.459168\pi\)
0.127925 + 0.991784i \(0.459168\pi\)
\(6\) −0.368135 −0.150291
\(7\) 0 0
\(8\) −1.42265 −0.502983
\(9\) 1.00000 0.333333
\(10\) 0.210609 0.0666005
\(11\) 5.73282 1.72851 0.864255 0.503055i \(-0.167791\pi\)
0.864255 + 0.503055i \(0.167791\pi\)
\(12\) 1.86448 0.538228
\(13\) 3.53946 0.981671 0.490835 0.871252i \(-0.336692\pi\)
0.490835 + 0.871252i \(0.336692\pi\)
\(14\) 0 0
\(15\) −0.572097 −0.147715
\(16\) 3.20522 0.801306
\(17\) 1.83305 0.444579 0.222289 0.974981i \(-0.428647\pi\)
0.222289 + 0.974981i \(0.428647\pi\)
\(18\) 0.368135 0.0867703
\(19\) 5.95881 1.36704 0.683522 0.729930i \(-0.260447\pi\)
0.683522 + 0.729930i \(0.260447\pi\)
\(20\) −1.06666 −0.238513
\(21\) 0 0
\(22\) 2.11045 0.449950
\(23\) 3.12066 0.650703 0.325351 0.945593i \(-0.394517\pi\)
0.325351 + 0.945593i \(0.394517\pi\)
\(24\) 1.42265 0.290397
\(25\) −4.67270 −0.934541
\(26\) 1.30300 0.255540
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −0.0143419 −0.00266322 −0.00133161 0.999999i \(-0.500424\pi\)
−0.00133161 + 0.999999i \(0.500424\pi\)
\(30\) −0.210609 −0.0384518
\(31\) −6.00517 −1.07856 −0.539281 0.842126i \(-0.681304\pi\)
−0.539281 + 0.842126i \(0.681304\pi\)
\(32\) 4.02526 0.711572
\(33\) −5.73282 −0.997955
\(34\) 0.674809 0.115729
\(35\) 0 0
\(36\) −1.86448 −0.310746
\(37\) 7.68699 1.26373 0.631867 0.775077i \(-0.282289\pi\)
0.631867 + 0.775077i \(0.282289\pi\)
\(38\) 2.19365 0.355857
\(39\) −3.53946 −0.566768
\(40\) −0.813895 −0.128688
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) 6.01972 0.917999 0.459000 0.888436i \(-0.348208\pi\)
0.459000 + 0.888436i \(0.348208\pi\)
\(44\) −10.6887 −1.61138
\(45\) 0.572097 0.0852833
\(46\) 1.14883 0.169385
\(47\) 6.07970 0.886815 0.443407 0.896320i \(-0.353769\pi\)
0.443407 + 0.896320i \(0.353769\pi\)
\(48\) −3.20522 −0.462634
\(49\) 0 0
\(50\) −1.72019 −0.243271
\(51\) −1.83305 −0.256678
\(52\) −6.59925 −0.915151
\(53\) −0.555156 −0.0762566 −0.0381283 0.999273i \(-0.512140\pi\)
−0.0381283 + 0.999273i \(0.512140\pi\)
\(54\) −0.368135 −0.0500969
\(55\) 3.27973 0.442239
\(56\) 0 0
\(57\) −5.95881 −0.789263
\(58\) −0.00527975 −0.000693265 0
\(59\) 7.46748 0.972182 0.486091 0.873908i \(-0.338422\pi\)
0.486091 + 0.873908i \(0.338422\pi\)
\(60\) 1.06666 0.137705
\(61\) −10.8150 −1.38472 −0.692360 0.721552i \(-0.743429\pi\)
−0.692360 + 0.721552i \(0.743429\pi\)
\(62\) −2.21072 −0.280761
\(63\) 0 0
\(64\) −4.92861 −0.616076
\(65\) 2.02492 0.251160
\(66\) −2.11045 −0.259779
\(67\) 3.12025 0.381199 0.190600 0.981668i \(-0.438957\pi\)
0.190600 + 0.981668i \(0.438957\pi\)
\(68\) −3.41767 −0.414453
\(69\) −3.12066 −0.375683
\(70\) 0 0
\(71\) −8.70596 −1.03321 −0.516603 0.856225i \(-0.672804\pi\)
−0.516603 + 0.856225i \(0.672804\pi\)
\(72\) −1.42265 −0.167661
\(73\) 8.02113 0.938803 0.469401 0.882985i \(-0.344470\pi\)
0.469401 + 0.882985i \(0.344470\pi\)
\(74\) 2.82985 0.328964
\(75\) 4.67270 0.539557
\(76\) −11.1101 −1.27441
\(77\) 0 0
\(78\) −1.30300 −0.147536
\(79\) 5.75556 0.647551 0.323775 0.946134i \(-0.395048\pi\)
0.323775 + 0.946134i \(0.395048\pi\)
\(80\) 1.83370 0.205014
\(81\) 1.00000 0.111111
\(82\) 0.368135 0.0406537
\(83\) −13.4857 −1.48025 −0.740124 0.672470i \(-0.765233\pi\)
−0.740124 + 0.672470i \(0.765233\pi\)
\(84\) 0 0
\(85\) 1.04868 0.113745
\(86\) 2.21607 0.238965
\(87\) 0.0143419 0.00153761
\(88\) −8.15579 −0.869410
\(89\) −2.84026 −0.301067 −0.150534 0.988605i \(-0.548099\pi\)
−0.150534 + 0.988605i \(0.548099\pi\)
\(90\) 0.210609 0.0222002
\(91\) 0 0
\(92\) −5.81840 −0.606610
\(93\) 6.00517 0.622708
\(94\) 2.23815 0.230848
\(95\) 3.40902 0.349758
\(96\) −4.02526 −0.410826
\(97\) −17.0640 −1.73259 −0.866295 0.499533i \(-0.833505\pi\)
−0.866295 + 0.499533i \(0.833505\pi\)
\(98\) 0 0
\(99\) 5.73282 0.576170
\(100\) 8.71215 0.871215
\(101\) 4.47011 0.444793 0.222396 0.974956i \(-0.428612\pi\)
0.222396 + 0.974956i \(0.428612\pi\)
\(102\) −0.674809 −0.0668160
\(103\) −14.9268 −1.47078 −0.735389 0.677645i \(-0.763001\pi\)
−0.735389 + 0.677645i \(0.763001\pi\)
\(104\) −5.03542 −0.493764
\(105\) 0 0
\(106\) −0.204373 −0.0198504
\(107\) −7.58526 −0.733294 −0.366647 0.930360i \(-0.619494\pi\)
−0.366647 + 0.930360i \(0.619494\pi\)
\(108\) 1.86448 0.179409
\(109\) −10.2791 −0.984555 −0.492277 0.870438i \(-0.663835\pi\)
−0.492277 + 0.870438i \(0.663835\pi\)
\(110\) 1.20738 0.115120
\(111\) −7.68699 −0.729617
\(112\) 0 0
\(113\) 12.2306 1.15056 0.575278 0.817958i \(-0.304894\pi\)
0.575278 + 0.817958i \(0.304894\pi\)
\(114\) −2.19365 −0.205454
\(115\) 1.78532 0.166482
\(116\) 0.0267401 0.00248275
\(117\) 3.53946 0.327224
\(118\) 2.74904 0.253070
\(119\) 0 0
\(120\) 0.813895 0.0742981
\(121\) 21.8652 1.98774
\(122\) −3.98139 −0.360458
\(123\) −1.00000 −0.0901670
\(124\) 11.1965 1.00548
\(125\) −5.53373 −0.494952
\(126\) 0 0
\(127\) −4.17403 −0.370386 −0.185193 0.982702i \(-0.559291\pi\)
−0.185193 + 0.982702i \(0.559291\pi\)
\(128\) −9.86491 −0.871943
\(129\) −6.01972 −0.530007
\(130\) 0.745444 0.0653798
\(131\) 9.28498 0.811233 0.405616 0.914043i \(-0.367057\pi\)
0.405616 + 0.914043i \(0.367057\pi\)
\(132\) 10.6887 0.930332
\(133\) 0 0
\(134\) 1.14867 0.0992303
\(135\) −0.572097 −0.0492383
\(136\) −2.60778 −0.223615
\(137\) −7.86277 −0.671762 −0.335881 0.941904i \(-0.609034\pi\)
−0.335881 + 0.941904i \(0.609034\pi\)
\(138\) −1.14883 −0.0977945
\(139\) −15.5406 −1.31814 −0.659068 0.752084i \(-0.729049\pi\)
−0.659068 + 0.752084i \(0.729049\pi\)
\(140\) 0 0
\(141\) −6.07970 −0.512003
\(142\) −3.20497 −0.268955
\(143\) 20.2911 1.69683
\(144\) 3.20522 0.267102
\(145\) −0.00820495 −0.000681384 0
\(146\) 2.95286 0.244381
\(147\) 0 0
\(148\) −14.3322 −1.17810
\(149\) 13.5549 1.11046 0.555231 0.831696i \(-0.312630\pi\)
0.555231 + 0.831696i \(0.312630\pi\)
\(150\) 1.72019 0.140453
\(151\) 11.5360 0.938787 0.469393 0.882989i \(-0.344473\pi\)
0.469393 + 0.882989i \(0.344473\pi\)
\(152\) −8.47730 −0.687600
\(153\) 1.83305 0.148193
\(154\) 0 0
\(155\) −3.43554 −0.275950
\(156\) 6.59925 0.528363
\(157\) 19.5905 1.56349 0.781744 0.623599i \(-0.214330\pi\)
0.781744 + 0.623599i \(0.214330\pi\)
\(158\) 2.11882 0.168565
\(159\) 0.555156 0.0440268
\(160\) 2.30284 0.182055
\(161\) 0 0
\(162\) 0.368135 0.0289234
\(163\) 15.5597 1.21873 0.609366 0.792889i \(-0.291424\pi\)
0.609366 + 0.792889i \(0.291424\pi\)
\(164\) −1.86448 −0.145591
\(165\) −3.27973 −0.255327
\(166\) −4.96456 −0.385325
\(167\) −5.56934 −0.430968 −0.215484 0.976507i \(-0.569133\pi\)
−0.215484 + 0.976507i \(0.569133\pi\)
\(168\) 0 0
\(169\) −0.472192 −0.0363224
\(170\) 0.386056 0.0296092
\(171\) 5.95881 0.455681
\(172\) −11.2236 −0.855794
\(173\) −6.77107 −0.514795 −0.257397 0.966306i \(-0.582865\pi\)
−0.257397 + 0.966306i \(0.582865\pi\)
\(174\) 0.00527975 0.000400257 0
\(175\) 0 0
\(176\) 18.3750 1.38507
\(177\) −7.46748 −0.561290
\(178\) −1.04560 −0.0783711
\(179\) 21.2999 1.59203 0.796014 0.605278i \(-0.206938\pi\)
0.796014 + 0.605278i \(0.206938\pi\)
\(180\) −1.06666 −0.0795043
\(181\) 1.68236 0.125049 0.0625246 0.998043i \(-0.480085\pi\)
0.0625246 + 0.998043i \(0.480085\pi\)
\(182\) 0 0
\(183\) 10.8150 0.799468
\(184\) −4.43961 −0.327292
\(185\) 4.39771 0.323326
\(186\) 2.21072 0.162098
\(187\) 10.5085 0.768458
\(188\) −11.3355 −0.826723
\(189\) 0 0
\(190\) 1.25498 0.0910458
\(191\) 23.4936 1.69994 0.849968 0.526834i \(-0.176621\pi\)
0.849968 + 0.526834i \(0.176621\pi\)
\(192\) 4.92861 0.355692
\(193\) −0.472321 −0.0339984 −0.0169992 0.999856i \(-0.505411\pi\)
−0.0169992 + 0.999856i \(0.505411\pi\)
\(194\) −6.28187 −0.451012
\(195\) −2.02492 −0.145007
\(196\) 0 0
\(197\) −10.4501 −0.744536 −0.372268 0.928125i \(-0.621420\pi\)
−0.372268 + 0.928125i \(0.621420\pi\)
\(198\) 2.11045 0.149983
\(199\) 17.6063 1.24808 0.624038 0.781394i \(-0.285491\pi\)
0.624038 + 0.781394i \(0.285491\pi\)
\(200\) 6.64762 0.470058
\(201\) −3.12025 −0.220085
\(202\) 1.64561 0.115784
\(203\) 0 0
\(204\) 3.41767 0.239285
\(205\) 0.572097 0.0399570
\(206\) −5.49507 −0.382860
\(207\) 3.12066 0.216901
\(208\) 11.3448 0.786619
\(209\) 34.1607 2.36295
\(210\) 0 0
\(211\) −2.47455 −0.170355 −0.0851774 0.996366i \(-0.527146\pi\)
−0.0851774 + 0.996366i \(0.527146\pi\)
\(212\) 1.03508 0.0710893
\(213\) 8.70596 0.596522
\(214\) −2.79240 −0.190885
\(215\) 3.44387 0.234870
\(216\) 1.42265 0.0967991
\(217\) 0 0
\(218\) −3.78408 −0.256290
\(219\) −8.02113 −0.542018
\(220\) −6.11498 −0.412272
\(221\) 6.48800 0.436430
\(222\) −2.82985 −0.189927
\(223\) 9.68745 0.648720 0.324360 0.945934i \(-0.394851\pi\)
0.324360 + 0.945934i \(0.394851\pi\)
\(224\) 0 0
\(225\) −4.67270 −0.311514
\(226\) 4.50251 0.299502
\(227\) −16.5132 −1.09602 −0.548011 0.836471i \(-0.684615\pi\)
−0.548011 + 0.836471i \(0.684615\pi\)
\(228\) 11.1101 0.735781
\(229\) −4.68553 −0.309629 −0.154814 0.987944i \(-0.549478\pi\)
−0.154814 + 0.987944i \(0.549478\pi\)
\(230\) 0.657240 0.0433371
\(231\) 0 0
\(232\) 0.0204035 0.00133955
\(233\) 15.5025 1.01560 0.507800 0.861475i \(-0.330459\pi\)
0.507800 + 0.861475i \(0.330459\pi\)
\(234\) 1.30300 0.0851799
\(235\) 3.47818 0.226891
\(236\) −13.9229 −0.906306
\(237\) −5.75556 −0.373864
\(238\) 0 0
\(239\) 26.7726 1.73178 0.865889 0.500236i \(-0.166753\pi\)
0.865889 + 0.500236i \(0.166753\pi\)
\(240\) −1.83370 −0.118365
\(241\) 10.1181 0.651766 0.325883 0.945410i \(-0.394338\pi\)
0.325883 + 0.945410i \(0.394338\pi\)
\(242\) 8.04935 0.517432
\(243\) −1.00000 −0.0641500
\(244\) 20.1643 1.29089
\(245\) 0 0
\(246\) −0.368135 −0.0234715
\(247\) 21.0910 1.34199
\(248\) 8.54326 0.542498
\(249\) 13.4857 0.854622
\(250\) −2.03716 −0.128841
\(251\) −18.7939 −1.18626 −0.593130 0.805107i \(-0.702108\pi\)
−0.593130 + 0.805107i \(0.702108\pi\)
\(252\) 0 0
\(253\) 17.8902 1.12475
\(254\) −1.53661 −0.0964155
\(255\) −1.04868 −0.0656709
\(256\) 6.22560 0.389100
\(257\) 9.48014 0.591355 0.295677 0.955288i \(-0.404455\pi\)
0.295677 + 0.955288i \(0.404455\pi\)
\(258\) −2.21607 −0.137967
\(259\) 0 0
\(260\) −3.77541 −0.234141
\(261\) −0.0143419 −0.000887740 0
\(262\) 3.41813 0.211173
\(263\) 26.2738 1.62011 0.810055 0.586354i \(-0.199437\pi\)
0.810055 + 0.586354i \(0.199437\pi\)
\(264\) 8.15579 0.501954
\(265\) −0.317604 −0.0195102
\(266\) 0 0
\(267\) 2.84026 0.173821
\(268\) −5.81763 −0.355368
\(269\) −7.74464 −0.472199 −0.236099 0.971729i \(-0.575869\pi\)
−0.236099 + 0.971729i \(0.575869\pi\)
\(270\) −0.210609 −0.0128173
\(271\) −19.3834 −1.17746 −0.588729 0.808331i \(-0.700371\pi\)
−0.588729 + 0.808331i \(0.700371\pi\)
\(272\) 5.87532 0.356244
\(273\) 0 0
\(274\) −2.89456 −0.174867
\(275\) −26.7878 −1.61536
\(276\) 5.81840 0.350226
\(277\) 2.76321 0.166025 0.0830125 0.996549i \(-0.473546\pi\)
0.0830125 + 0.996549i \(0.473546\pi\)
\(278\) −5.72104 −0.343125
\(279\) −6.00517 −0.359520
\(280\) 0 0
\(281\) 23.5677 1.40593 0.702967 0.711223i \(-0.251858\pi\)
0.702967 + 0.711223i \(0.251858\pi\)
\(282\) −2.23815 −0.133280
\(283\) −30.7005 −1.82495 −0.912476 0.409130i \(-0.865832\pi\)
−0.912476 + 0.409130i \(0.865832\pi\)
\(284\) 16.2320 0.963195
\(285\) −3.40902 −0.201933
\(286\) 7.46987 0.441703
\(287\) 0 0
\(288\) 4.02526 0.237191
\(289\) −13.6399 −0.802350
\(290\) −0.00302053 −0.000177372 0
\(291\) 17.0640 1.00031
\(292\) −14.9552 −0.875188
\(293\) −2.03371 −0.118810 −0.0594052 0.998234i \(-0.518920\pi\)
−0.0594052 + 0.998234i \(0.518920\pi\)
\(294\) 0 0
\(295\) 4.27212 0.248733
\(296\) −10.9359 −0.635637
\(297\) −5.73282 −0.332652
\(298\) 4.99005 0.289066
\(299\) 11.0455 0.638776
\(300\) −8.71215 −0.502996
\(301\) 0 0
\(302\) 4.24681 0.244376
\(303\) −4.47011 −0.256801
\(304\) 19.0993 1.09542
\(305\) −6.18724 −0.354280
\(306\) 0.674809 0.0385762
\(307\) 1.78236 0.101725 0.0508623 0.998706i \(-0.483803\pi\)
0.0508623 + 0.998706i \(0.483803\pi\)
\(308\) 0 0
\(309\) 14.9268 0.849154
\(310\) −1.26475 −0.0718327
\(311\) −12.2745 −0.696021 −0.348011 0.937491i \(-0.613143\pi\)
−0.348011 + 0.937491i \(0.613143\pi\)
\(312\) 5.03542 0.285075
\(313\) −3.15436 −0.178295 −0.0891475 0.996018i \(-0.528414\pi\)
−0.0891475 + 0.996018i \(0.528414\pi\)
\(314\) 7.21194 0.406993
\(315\) 0 0
\(316\) −10.7311 −0.603672
\(317\) −6.09319 −0.342228 −0.171114 0.985251i \(-0.554737\pi\)
−0.171114 + 0.985251i \(0.554737\pi\)
\(318\) 0.204373 0.0114607
\(319\) −0.0822193 −0.00460340
\(320\) −2.81965 −0.157623
\(321\) 7.58526 0.423368
\(322\) 0 0
\(323\) 10.9228 0.607759
\(324\) −1.86448 −0.103582
\(325\) −16.5389 −0.917412
\(326\) 5.72809 0.317249
\(327\) 10.2791 0.568433
\(328\) −1.42265 −0.0785527
\(329\) 0 0
\(330\) −1.20738 −0.0664643
\(331\) 30.2082 1.66039 0.830195 0.557473i \(-0.188229\pi\)
0.830195 + 0.557473i \(0.188229\pi\)
\(332\) 25.1438 1.37994
\(333\) 7.68699 0.421245
\(334\) −2.05027 −0.112186
\(335\) 1.78509 0.0975297
\(336\) 0 0
\(337\) −15.4472 −0.841463 −0.420731 0.907185i \(-0.638227\pi\)
−0.420731 + 0.907185i \(0.638227\pi\)
\(338\) −0.173830 −0.00945513
\(339\) −12.2306 −0.664274
\(340\) −1.95524 −0.106038
\(341\) −34.4266 −1.86430
\(342\) 2.19365 0.118619
\(343\) 0 0
\(344\) −8.56396 −0.461738
\(345\) −1.78532 −0.0961185
\(346\) −2.49267 −0.134007
\(347\) −31.1378 −1.67156 −0.835781 0.549062i \(-0.814985\pi\)
−0.835781 + 0.549062i \(0.814985\pi\)
\(348\) −0.0267401 −0.00143342
\(349\) 14.4496 0.773470 0.386735 0.922191i \(-0.373603\pi\)
0.386735 + 0.922191i \(0.373603\pi\)
\(350\) 0 0
\(351\) −3.53946 −0.188923
\(352\) 23.0761 1.22996
\(353\) 17.1005 0.910169 0.455085 0.890448i \(-0.349609\pi\)
0.455085 + 0.890448i \(0.349609\pi\)
\(354\) −2.74904 −0.146110
\(355\) −4.98066 −0.264346
\(356\) 5.29560 0.280666
\(357\) 0 0
\(358\) 7.84124 0.414423
\(359\) 28.1115 1.48367 0.741833 0.670585i \(-0.233957\pi\)
0.741833 + 0.670585i \(0.233957\pi\)
\(360\) −0.813895 −0.0428960
\(361\) 16.5074 0.868810
\(362\) 0.619337 0.0325517
\(363\) −21.8652 −1.14762
\(364\) 0 0
\(365\) 4.58887 0.240192
\(366\) 3.98139 0.208110
\(367\) 8.76594 0.457578 0.228789 0.973476i \(-0.426523\pi\)
0.228789 + 0.973476i \(0.426523\pi\)
\(368\) 10.0024 0.521412
\(369\) 1.00000 0.0520579
\(370\) 1.61895 0.0841653
\(371\) 0 0
\(372\) −11.1965 −0.580512
\(373\) 4.95495 0.256558 0.128279 0.991738i \(-0.459055\pi\)
0.128279 + 0.991738i \(0.459055\pi\)
\(374\) 3.86855 0.200038
\(375\) 5.53373 0.285761
\(376\) −8.64928 −0.446053
\(377\) −0.0507625 −0.00261440
\(378\) 0 0
\(379\) −18.2578 −0.937841 −0.468921 0.883240i \(-0.655357\pi\)
−0.468921 + 0.883240i \(0.655357\pi\)
\(380\) −6.35603 −0.326058
\(381\) 4.17403 0.213842
\(382\) 8.64882 0.442512
\(383\) 4.11599 0.210317 0.105159 0.994455i \(-0.466465\pi\)
0.105159 + 0.994455i \(0.466465\pi\)
\(384\) 9.86491 0.503417
\(385\) 0 0
\(386\) −0.173878 −0.00885016
\(387\) 6.01972 0.306000
\(388\) 31.8155 1.61519
\(389\) −38.8864 −1.97162 −0.985809 0.167870i \(-0.946311\pi\)
−0.985809 + 0.167870i \(0.946311\pi\)
\(390\) −0.745444 −0.0377470
\(391\) 5.72031 0.289289
\(392\) 0 0
\(393\) −9.28498 −0.468365
\(394\) −3.84704 −0.193811
\(395\) 3.29274 0.165676
\(396\) −10.6887 −0.537127
\(397\) −7.84996 −0.393978 −0.196989 0.980406i \(-0.563116\pi\)
−0.196989 + 0.980406i \(0.563116\pi\)
\(398\) 6.48149 0.324888
\(399\) 0 0
\(400\) −14.9771 −0.748853
\(401\) 12.7903 0.638717 0.319358 0.947634i \(-0.396533\pi\)
0.319358 + 0.947634i \(0.396533\pi\)
\(402\) −1.14867 −0.0572907
\(403\) −21.2551 −1.05879
\(404\) −8.33442 −0.414653
\(405\) 0.572097 0.0284278
\(406\) 0 0
\(407\) 44.0681 2.18438
\(408\) 2.60778 0.129104
\(409\) −16.1403 −0.798086 −0.399043 0.916932i \(-0.630658\pi\)
−0.399043 + 0.916932i \(0.630658\pi\)
\(410\) 0.210609 0.0104013
\(411\) 7.86277 0.387842
\(412\) 27.8306 1.37112
\(413\) 0 0
\(414\) 1.14883 0.0564617
\(415\) −7.71513 −0.378721
\(416\) 14.2473 0.698529
\(417\) 15.5406 0.761026
\(418\) 12.5758 0.615101
\(419\) −20.6228 −1.00749 −0.503745 0.863852i \(-0.668045\pi\)
−0.503745 + 0.863852i \(0.668045\pi\)
\(420\) 0 0
\(421\) 21.8239 1.06363 0.531815 0.846861i \(-0.321510\pi\)
0.531815 + 0.846861i \(0.321510\pi\)
\(422\) −0.910968 −0.0443452
\(423\) 6.07970 0.295605
\(424\) 0.789794 0.0383558
\(425\) −8.56528 −0.415477
\(426\) 3.20497 0.155281
\(427\) 0 0
\(428\) 14.1425 0.683605
\(429\) −20.2911 −0.979664
\(430\) 1.26781 0.0611392
\(431\) −32.1389 −1.54808 −0.774039 0.633138i \(-0.781766\pi\)
−0.774039 + 0.633138i \(0.781766\pi\)
\(432\) −3.20522 −0.154211
\(433\) 5.26215 0.252883 0.126441 0.991974i \(-0.459644\pi\)
0.126441 + 0.991974i \(0.459644\pi\)
\(434\) 0 0
\(435\) 0.00820495 0.000393397 0
\(436\) 19.1651 0.917839
\(437\) 18.5954 0.889539
\(438\) −2.95286 −0.141093
\(439\) −4.85141 −0.231545 −0.115773 0.993276i \(-0.536934\pi\)
−0.115773 + 0.993276i \(0.536934\pi\)
\(440\) −4.66591 −0.222438
\(441\) 0 0
\(442\) 2.38846 0.113608
\(443\) 1.60189 0.0761083 0.0380541 0.999276i \(-0.487884\pi\)
0.0380541 + 0.999276i \(0.487884\pi\)
\(444\) 14.3322 0.680177
\(445\) −1.62491 −0.0770280
\(446\) 3.56629 0.168869
\(447\) −13.5549 −0.641126
\(448\) 0 0
\(449\) −0.340029 −0.0160470 −0.00802348 0.999968i \(-0.502554\pi\)
−0.00802348 + 0.999968i \(0.502554\pi\)
\(450\) −1.72019 −0.0810904
\(451\) 5.73282 0.269948
\(452\) −22.8036 −1.07259
\(453\) −11.5360 −0.542009
\(454\) −6.07911 −0.285307
\(455\) 0 0
\(456\) 8.47730 0.396986
\(457\) 5.27444 0.246728 0.123364 0.992362i \(-0.460632\pi\)
0.123364 + 0.992362i \(0.460632\pi\)
\(458\) −1.72491 −0.0805997
\(459\) −1.83305 −0.0855592
\(460\) −3.32869 −0.155201
\(461\) 19.2751 0.897731 0.448866 0.893599i \(-0.351828\pi\)
0.448866 + 0.893599i \(0.351828\pi\)
\(462\) 0 0
\(463\) 36.5289 1.69764 0.848820 0.528682i \(-0.177314\pi\)
0.848820 + 0.528682i \(0.177314\pi\)
\(464\) −0.0459689 −0.00213405
\(465\) 3.43554 0.159320
\(466\) 5.70700 0.264372
\(467\) −28.2161 −1.30569 −0.652843 0.757493i \(-0.726424\pi\)
−0.652843 + 0.757493i \(0.726424\pi\)
\(468\) −6.59925 −0.305050
\(469\) 0 0
\(470\) 1.28044 0.0590623
\(471\) −19.5905 −0.902681
\(472\) −10.6236 −0.488991
\(473\) 34.5100 1.58677
\(474\) −2.11882 −0.0973208
\(475\) −27.8437 −1.27756
\(476\) 0 0
\(477\) −0.555156 −0.0254189
\(478\) 9.85595 0.450801
\(479\) −21.9430 −1.00260 −0.501300 0.865274i \(-0.667145\pi\)
−0.501300 + 0.865274i \(0.667145\pi\)
\(480\) −2.30284 −0.105110
\(481\) 27.2078 1.24057
\(482\) 3.72484 0.169662
\(483\) 0 0
\(484\) −40.7671 −1.85305
\(485\) −9.76229 −0.443283
\(486\) −0.368135 −0.0166990
\(487\) −21.5895 −0.978314 −0.489157 0.872196i \(-0.662696\pi\)
−0.489157 + 0.872196i \(0.662696\pi\)
\(488\) 15.3860 0.696490
\(489\) −15.5597 −0.703636
\(490\) 0 0
\(491\) −38.4173 −1.73375 −0.866874 0.498527i \(-0.833874\pi\)
−0.866874 + 0.498527i \(0.833874\pi\)
\(492\) 1.86448 0.0840571
\(493\) −0.0262893 −0.00118401
\(494\) 7.76434 0.349334
\(495\) 3.27973 0.147413
\(496\) −19.2479 −0.864258
\(497\) 0 0
\(498\) 4.96456 0.222467
\(499\) −11.8858 −0.532083 −0.266042 0.963962i \(-0.585716\pi\)
−0.266042 + 0.963962i \(0.585716\pi\)
\(500\) 10.3175 0.461413
\(501\) 5.56934 0.248820
\(502\) −6.91869 −0.308796
\(503\) −8.91377 −0.397445 −0.198723 0.980056i \(-0.563679\pi\)
−0.198723 + 0.980056i \(0.563679\pi\)
\(504\) 0 0
\(505\) 2.55734 0.113800
\(506\) 6.58601 0.292784
\(507\) 0.472192 0.0209708
\(508\) 7.78239 0.345288
\(509\) 22.7887 1.01009 0.505046 0.863093i \(-0.331476\pi\)
0.505046 + 0.863093i \(0.331476\pi\)
\(510\) −0.386056 −0.0170949
\(511\) 0 0
\(512\) 22.0217 0.973230
\(513\) −5.95881 −0.263088
\(514\) 3.48997 0.153936
\(515\) −8.53957 −0.376298
\(516\) 11.2236 0.494093
\(517\) 34.8538 1.53287
\(518\) 0 0
\(519\) 6.77107 0.297217
\(520\) −2.88075 −0.126329
\(521\) 21.7252 0.951800 0.475900 0.879499i \(-0.342122\pi\)
0.475900 + 0.879499i \(0.342122\pi\)
\(522\) −0.00527975 −0.000231088 0
\(523\) 44.0260 1.92512 0.962562 0.271061i \(-0.0873746\pi\)
0.962562 + 0.271061i \(0.0873746\pi\)
\(524\) −17.3116 −0.756262
\(525\) 0 0
\(526\) 9.67230 0.421733
\(527\) −11.0078 −0.479505
\(528\) −18.3750 −0.799668
\(529\) −13.2615 −0.576586
\(530\) −0.116921 −0.00507873
\(531\) 7.46748 0.324061
\(532\) 0 0
\(533\) 3.53946 0.153311
\(534\) 1.04560 0.0452476
\(535\) −4.33951 −0.187613
\(536\) −4.43902 −0.191737
\(537\) −21.2999 −0.919158
\(538\) −2.85107 −0.122919
\(539\) 0 0
\(540\) 1.06666 0.0459018
\(541\) 28.2078 1.21275 0.606373 0.795180i \(-0.292624\pi\)
0.606373 + 0.795180i \(0.292624\pi\)
\(542\) −7.13571 −0.306505
\(543\) −1.68236 −0.0721971
\(544\) 7.37848 0.316350
\(545\) −5.88062 −0.251898
\(546\) 0 0
\(547\) 13.0668 0.558694 0.279347 0.960190i \(-0.409882\pi\)
0.279347 + 0.960190i \(0.409882\pi\)
\(548\) 14.6600 0.626242
\(549\) −10.8150 −0.461573
\(550\) −9.86152 −0.420497
\(551\) −0.0854605 −0.00364074
\(552\) 4.43961 0.188962
\(553\) 0 0
\(554\) 1.01723 0.0432181
\(555\) −4.39771 −0.186672
\(556\) 28.9751 1.22882
\(557\) −0.655721 −0.0277838 −0.0138919 0.999904i \(-0.504422\pi\)
−0.0138919 + 0.999904i \(0.504422\pi\)
\(558\) −2.21072 −0.0935871
\(559\) 21.3066 0.901173
\(560\) 0 0
\(561\) −10.5085 −0.443670
\(562\) 8.67612 0.365980
\(563\) −11.5086 −0.485028 −0.242514 0.970148i \(-0.577972\pi\)
−0.242514 + 0.970148i \(0.577972\pi\)
\(564\) 11.3355 0.477309
\(565\) 6.99708 0.294369
\(566\) −11.3019 −0.475055
\(567\) 0 0
\(568\) 12.3855 0.519685
\(569\) −21.4649 −0.899854 −0.449927 0.893065i \(-0.648550\pi\)
−0.449927 + 0.893065i \(0.648550\pi\)
\(570\) −1.25498 −0.0525653
\(571\) −4.64258 −0.194286 −0.0971429 0.995270i \(-0.530970\pi\)
−0.0971429 + 0.995270i \(0.530970\pi\)
\(572\) −37.8323 −1.58185
\(573\) −23.4936 −0.981459
\(574\) 0 0
\(575\) −14.5819 −0.608108
\(576\) −4.92861 −0.205359
\(577\) −7.53651 −0.313749 −0.156875 0.987619i \(-0.550142\pi\)
−0.156875 + 0.987619i \(0.550142\pi\)
\(578\) −5.02135 −0.208860
\(579\) 0.472321 0.0196290
\(580\) 0.0152979 0.000635212 0
\(581\) 0 0
\(582\) 6.28187 0.260392
\(583\) −3.18261 −0.131810
\(584\) −11.4113 −0.472202
\(585\) 2.02492 0.0837201
\(586\) −0.748679 −0.0309277
\(587\) −27.6511 −1.14128 −0.570641 0.821200i \(-0.693305\pi\)
−0.570641 + 0.821200i \(0.693305\pi\)
\(588\) 0 0
\(589\) −35.7837 −1.47444
\(590\) 1.57272 0.0647478
\(591\) 10.4501 0.429858
\(592\) 24.6385 1.01264
\(593\) −15.7715 −0.647658 −0.323829 0.946116i \(-0.604970\pi\)
−0.323829 + 0.946116i \(0.604970\pi\)
\(594\) −2.11045 −0.0865929
\(595\) 0 0
\(596\) −25.2728 −1.03522
\(597\) −17.6063 −0.720577
\(598\) 4.06623 0.166280
\(599\) −23.6599 −0.966716 −0.483358 0.875423i \(-0.660583\pi\)
−0.483358 + 0.875423i \(0.660583\pi\)
\(600\) −6.64762 −0.271388
\(601\) 28.5440 1.16433 0.582166 0.813070i \(-0.302205\pi\)
0.582166 + 0.813070i \(0.302205\pi\)
\(602\) 0 0
\(603\) 3.12025 0.127066
\(604\) −21.5086 −0.875173
\(605\) 12.5090 0.508564
\(606\) −1.64561 −0.0668482
\(607\) −8.51374 −0.345562 −0.172781 0.984960i \(-0.555275\pi\)
−0.172781 + 0.984960i \(0.555275\pi\)
\(608\) 23.9857 0.972750
\(609\) 0 0
\(610\) −2.27774 −0.0922230
\(611\) 21.5189 0.870560
\(612\) −3.41767 −0.138151
\(613\) −2.53249 −0.102286 −0.0511431 0.998691i \(-0.516286\pi\)
−0.0511431 + 0.998691i \(0.516286\pi\)
\(614\) 0.656149 0.0264800
\(615\) −0.572097 −0.0230692
\(616\) 0 0
\(617\) −16.5279 −0.665387 −0.332694 0.943035i \(-0.607957\pi\)
−0.332694 + 0.943035i \(0.607957\pi\)
\(618\) 5.49507 0.221044
\(619\) 17.3928 0.699075 0.349537 0.936922i \(-0.386339\pi\)
0.349537 + 0.936922i \(0.386339\pi\)
\(620\) 6.40549 0.257251
\(621\) −3.12066 −0.125228
\(622\) −4.51867 −0.181182
\(623\) 0 0
\(624\) −11.3448 −0.454155
\(625\) 20.1977 0.807908
\(626\) −1.16123 −0.0464122
\(627\) −34.1607 −1.36425
\(628\) −36.5259 −1.45754
\(629\) 14.0906 0.561829
\(630\) 0 0
\(631\) −38.3799 −1.52788 −0.763940 0.645287i \(-0.776738\pi\)
−0.763940 + 0.645287i \(0.776738\pi\)
\(632\) −8.18815 −0.325707
\(633\) 2.47455 0.0983544
\(634\) −2.24312 −0.0890857
\(635\) −2.38795 −0.0947631
\(636\) −1.03508 −0.0410434
\(637\) 0 0
\(638\) −0.0302678 −0.00119832
\(639\) −8.70596 −0.344402
\(640\) −5.64369 −0.223086
\(641\) 12.4300 0.490955 0.245477 0.969402i \(-0.421055\pi\)
0.245477 + 0.969402i \(0.421055\pi\)
\(642\) 2.79240 0.110207
\(643\) 15.1428 0.597172 0.298586 0.954383i \(-0.403485\pi\)
0.298586 + 0.954383i \(0.403485\pi\)
\(644\) 0 0
\(645\) −3.44387 −0.135602
\(646\) 4.02105 0.158206
\(647\) −12.5947 −0.495149 −0.247574 0.968869i \(-0.579633\pi\)
−0.247574 + 0.968869i \(0.579633\pi\)
\(648\) −1.42265 −0.0558870
\(649\) 42.8097 1.68043
\(650\) −6.08854 −0.238812
\(651\) 0 0
\(652\) −29.0108 −1.13615
\(653\) −20.3273 −0.795467 −0.397734 0.917501i \(-0.630203\pi\)
−0.397734 + 0.917501i \(0.630203\pi\)
\(654\) 3.78408 0.147969
\(655\) 5.31191 0.207554
\(656\) 3.20522 0.125143
\(657\) 8.02113 0.312934
\(658\) 0 0
\(659\) 20.2304 0.788063 0.394031 0.919097i \(-0.371080\pi\)
0.394031 + 0.919097i \(0.371080\pi\)
\(660\) 6.11498 0.238025
\(661\) 29.3691 1.14233 0.571163 0.820837i \(-0.306492\pi\)
0.571163 + 0.820837i \(0.306492\pi\)
\(662\) 11.1207 0.432218
\(663\) −6.48800 −0.251973
\(664\) 19.1854 0.744539
\(665\) 0 0
\(666\) 2.82985 0.109655
\(667\) −0.0447561 −0.00173296
\(668\) 10.3839 0.401765
\(669\) −9.68745 −0.374539
\(670\) 0.657154 0.0253881
\(671\) −62.0005 −2.39350
\(672\) 0 0
\(673\) 32.9695 1.27088 0.635441 0.772150i \(-0.280818\pi\)
0.635441 + 0.772150i \(0.280818\pi\)
\(674\) −5.68666 −0.219042
\(675\) 4.67270 0.179852
\(676\) 0.880390 0.0338612
\(677\) 31.1088 1.19561 0.597805 0.801642i \(-0.296040\pi\)
0.597805 + 0.801642i \(0.296040\pi\)
\(678\) −4.50251 −0.172918
\(679\) 0 0
\(680\) −1.49191 −0.0572120
\(681\) 16.5132 0.632789
\(682\) −12.6736 −0.485298
\(683\) 27.6060 1.05632 0.528158 0.849146i \(-0.322883\pi\)
0.528158 + 0.849146i \(0.322883\pi\)
\(684\) −11.1101 −0.424804
\(685\) −4.49827 −0.171870
\(686\) 0 0
\(687\) 4.68553 0.178764
\(688\) 19.2946 0.735599
\(689\) −1.96496 −0.0748589
\(690\) −0.657240 −0.0250207
\(691\) 12.7292 0.484240 0.242120 0.970246i \(-0.422157\pi\)
0.242120 + 0.970246i \(0.422157\pi\)
\(692\) 12.6245 0.479911
\(693\) 0 0
\(694\) −11.4629 −0.435126
\(695\) −8.89073 −0.337245
\(696\) −0.0204035 −0.000773392 0
\(697\) 1.83305 0.0694315
\(698\) 5.31942 0.201343
\(699\) −15.5025 −0.586357
\(700\) 0 0
\(701\) −34.6716 −1.30953 −0.654765 0.755832i \(-0.727232\pi\)
−0.654765 + 0.755832i \(0.727232\pi\)
\(702\) −1.30300 −0.0491786
\(703\) 45.8053 1.72758
\(704\) −28.2548 −1.06489
\(705\) −3.47818 −0.130996
\(706\) 6.29531 0.236927
\(707\) 0 0
\(708\) 13.9229 0.523256
\(709\) −25.5878 −0.960969 −0.480484 0.877003i \(-0.659539\pi\)
−0.480484 + 0.877003i \(0.659539\pi\)
\(710\) −1.83356 −0.0688121
\(711\) 5.75556 0.215850
\(712\) 4.04070 0.151432
\(713\) −18.7401 −0.701823
\(714\) 0 0
\(715\) 11.6085 0.434133
\(716\) −39.7131 −1.48415
\(717\) −26.7726 −0.999843
\(718\) 10.3488 0.386215
\(719\) −16.6471 −0.620832 −0.310416 0.950601i \(-0.600468\pi\)
−0.310416 + 0.950601i \(0.600468\pi\)
\(720\) 1.83370 0.0683380
\(721\) 0 0
\(722\) 6.07695 0.226161
\(723\) −10.1181 −0.376297
\(724\) −3.13673 −0.116576
\(725\) 0.0670153 0.00248889
\(726\) −8.04935 −0.298739
\(727\) 49.3359 1.82977 0.914883 0.403720i \(-0.132283\pi\)
0.914883 + 0.403720i \(0.132283\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 1.68933 0.0625247
\(731\) 11.0344 0.408123
\(732\) −20.1643 −0.745295
\(733\) 35.2802 1.30311 0.651553 0.758603i \(-0.274118\pi\)
0.651553 + 0.758603i \(0.274118\pi\)
\(734\) 3.22705 0.119113
\(735\) 0 0
\(736\) 12.5615 0.463022
\(737\) 17.8878 0.658906
\(738\) 0.368135 0.0135512
\(739\) −13.1321 −0.483071 −0.241535 0.970392i \(-0.577651\pi\)
−0.241535 + 0.970392i \(0.577651\pi\)
\(740\) −8.19943 −0.301417
\(741\) −21.0910 −0.774797
\(742\) 0 0
\(743\) −35.4339 −1.29994 −0.649971 0.759959i \(-0.725219\pi\)
−0.649971 + 0.759959i \(0.725219\pi\)
\(744\) −8.54326 −0.313211
\(745\) 7.75474 0.284112
\(746\) 1.82409 0.0667848
\(747\) −13.4857 −0.493416
\(748\) −19.5929 −0.716386
\(749\) 0 0
\(750\) 2.03716 0.0743866
\(751\) 34.6635 1.26489 0.632445 0.774606i \(-0.282052\pi\)
0.632445 + 0.774606i \(0.282052\pi\)
\(752\) 19.4868 0.710610
\(753\) 18.7939 0.684887
\(754\) −0.0186875 −0.000680558 0
\(755\) 6.59972 0.240188
\(756\) 0 0
\(757\) 44.3224 1.61093 0.805463 0.592646i \(-0.201917\pi\)
0.805463 + 0.592646i \(0.201917\pi\)
\(758\) −6.72135 −0.244130
\(759\) −17.8902 −0.649372
\(760\) −4.84984 −0.175922
\(761\) −5.89442 −0.213673 −0.106836 0.994277i \(-0.534072\pi\)
−0.106836 + 0.994277i \(0.534072\pi\)
\(762\) 1.53661 0.0556655
\(763\) 0 0
\(764\) −43.8032 −1.58475
\(765\) 1.04868 0.0379151
\(766\) 1.51524 0.0547479
\(767\) 26.4309 0.954363
\(768\) −6.22560 −0.224647
\(769\) −23.7197 −0.855355 −0.427678 0.903931i \(-0.640668\pi\)
−0.427678 + 0.903931i \(0.640668\pi\)
\(770\) 0 0
\(771\) −9.48014 −0.341419
\(772\) 0.880632 0.0316946
\(773\) 31.9035 1.14749 0.573745 0.819034i \(-0.305490\pi\)
0.573745 + 0.819034i \(0.305490\pi\)
\(774\) 2.21607 0.0796551
\(775\) 28.0604 1.00796
\(776\) 24.2762 0.871463
\(777\) 0 0
\(778\) −14.3155 −0.513234
\(779\) 5.95881 0.213496
\(780\) 3.77541 0.135181
\(781\) −49.9096 −1.78591
\(782\) 2.10585 0.0753050
\(783\) 0.0143419 0.000512537 0
\(784\) 0 0
\(785\) 11.2077 0.400018
\(786\) −3.41813 −0.121921
\(787\) 29.8518 1.06410 0.532050 0.846713i \(-0.321422\pi\)
0.532050 + 0.846713i \(0.321422\pi\)
\(788\) 19.4839 0.694085
\(789\) −26.2738 −0.935371
\(790\) 1.21217 0.0431272
\(791\) 0 0
\(792\) −8.15579 −0.289803
\(793\) −38.2793 −1.35934
\(794\) −2.88985 −0.102557
\(795\) 0.317604 0.0112642
\(796\) −32.8265 −1.16350
\(797\) −12.8988 −0.456898 −0.228449 0.973556i \(-0.573365\pi\)
−0.228449 + 0.973556i \(0.573365\pi\)
\(798\) 0 0
\(799\) 11.1444 0.394259
\(800\) −18.8088 −0.664993
\(801\) −2.84026 −0.100356
\(802\) 4.70856 0.166265
\(803\) 45.9837 1.62273
\(804\) 5.81763 0.205172
\(805\) 0 0
\(806\) −7.82475 −0.275615
\(807\) 7.74464 0.272624
\(808\) −6.35941 −0.223723
\(809\) −46.4983 −1.63479 −0.817396 0.576075i \(-0.804583\pi\)
−0.817396 + 0.576075i \(0.804583\pi\)
\(810\) 0.210609 0.00740006
\(811\) −35.2925 −1.23929 −0.619643 0.784883i \(-0.712723\pi\)
−0.619643 + 0.784883i \(0.712723\pi\)
\(812\) 0 0
\(813\) 19.3834 0.679805
\(814\) 16.2230 0.568617
\(815\) 8.90168 0.311812
\(816\) −5.87532 −0.205677
\(817\) 35.8704 1.25495
\(818\) −5.94181 −0.207751
\(819\) 0 0
\(820\) −1.06666 −0.0372495
\(821\) −16.2632 −0.567590 −0.283795 0.958885i \(-0.591594\pi\)
−0.283795 + 0.958885i \(0.591594\pi\)
\(822\) 2.89456 0.100960
\(823\) 28.4263 0.990880 0.495440 0.868642i \(-0.335007\pi\)
0.495440 + 0.868642i \(0.335007\pi\)
\(824\) 21.2356 0.739776
\(825\) 26.7878 0.932630
\(826\) 0 0
\(827\) 36.3536 1.26414 0.632070 0.774911i \(-0.282205\pi\)
0.632070 + 0.774911i \(0.282205\pi\)
\(828\) −5.81840 −0.202203
\(829\) −43.8325 −1.52236 −0.761182 0.648538i \(-0.775381\pi\)
−0.761182 + 0.648538i \(0.775381\pi\)
\(830\) −2.84021 −0.0985853
\(831\) −2.76321 −0.0958545
\(832\) −17.4446 −0.604784
\(833\) 0 0
\(834\) 5.72104 0.198103
\(835\) −3.18620 −0.110263
\(836\) −63.6919 −2.20283
\(837\) 6.00517 0.207569
\(838\) −7.59198 −0.262261
\(839\) 35.7789 1.23523 0.617613 0.786482i \(-0.288100\pi\)
0.617613 + 0.786482i \(0.288100\pi\)
\(840\) 0 0
\(841\) −28.9998 −0.999993
\(842\) 8.03413 0.276874
\(843\) −23.5677 −0.811716
\(844\) 4.61373 0.158811
\(845\) −0.270140 −0.00929309
\(846\) 2.23815 0.0769492
\(847\) 0 0
\(848\) −1.77940 −0.0611049
\(849\) 30.7005 1.05364
\(850\) −3.15318 −0.108153
\(851\) 23.9885 0.822315
\(852\) −16.2320 −0.556101
\(853\) 9.95627 0.340896 0.170448 0.985367i \(-0.445478\pi\)
0.170448 + 0.985367i \(0.445478\pi\)
\(854\) 0 0
\(855\) 3.40902 0.116586
\(856\) 10.7912 0.368834
\(857\) −39.7735 −1.35864 −0.679319 0.733843i \(-0.737725\pi\)
−0.679319 + 0.733843i \(0.737725\pi\)
\(858\) −7.46987 −0.255017
\(859\) 21.4817 0.732947 0.366474 0.930428i \(-0.380565\pi\)
0.366474 + 0.930428i \(0.380565\pi\)
\(860\) −6.42101 −0.218955
\(861\) 0 0
\(862\) −11.8315 −0.402982
\(863\) 14.9202 0.507889 0.253945 0.967219i \(-0.418272\pi\)
0.253945 + 0.967219i \(0.418272\pi\)
\(864\) −4.02526 −0.136942
\(865\) −3.87371 −0.131710
\(866\) 1.93718 0.0658282
\(867\) 13.6399 0.463237
\(868\) 0 0
\(869\) 32.9956 1.11930
\(870\) 0.00302053 0.000102406 0
\(871\) 11.0440 0.374212
\(872\) 14.6235 0.495214
\(873\) −17.0640 −0.577530
\(874\) 6.84563 0.231557
\(875\) 0 0
\(876\) 14.9552 0.505290
\(877\) 14.4102 0.486599 0.243299 0.969951i \(-0.421770\pi\)
0.243299 + 0.969951i \(0.421770\pi\)
\(878\) −1.78598 −0.0602738
\(879\) 2.03371 0.0685952
\(880\) 10.5123 0.354369
\(881\) 16.5606 0.557942 0.278971 0.960300i \(-0.410007\pi\)
0.278971 + 0.960300i \(0.410007\pi\)
\(882\) 0 0
\(883\) −45.1125 −1.51815 −0.759077 0.651000i \(-0.774350\pi\)
−0.759077 + 0.651000i \(0.774350\pi\)
\(884\) −12.0967 −0.406857
\(885\) −4.27212 −0.143606
\(886\) 0.589714 0.0198118
\(887\) 1.62359 0.0545150 0.0272575 0.999628i \(-0.491323\pi\)
0.0272575 + 0.999628i \(0.491323\pi\)
\(888\) 10.9359 0.366985
\(889\) 0 0
\(890\) −0.598186 −0.0200512
\(891\) 5.73282 0.192057
\(892\) −18.0620 −0.604761
\(893\) 36.2277 1.21232
\(894\) −4.99005 −0.166892
\(895\) 12.1856 0.407320
\(896\) 0 0
\(897\) −11.0455 −0.368797
\(898\) −0.125177 −0.00417720
\(899\) 0.0861254 0.00287244
\(900\) 8.71215 0.290405
\(901\) −1.01763 −0.0339021
\(902\) 2.11045 0.0702704
\(903\) 0 0
\(904\) −17.3998 −0.578710
\(905\) 0.962476 0.0319938
\(906\) −4.24681 −0.141091
\(907\) −51.5666 −1.71224 −0.856120 0.516777i \(-0.827132\pi\)
−0.856120 + 0.516777i \(0.827132\pi\)
\(908\) 30.7885 1.02175
\(909\) 4.47011 0.148264
\(910\) 0 0
\(911\) 38.8580 1.28742 0.643712 0.765268i \(-0.277394\pi\)
0.643712 + 0.765268i \(0.277394\pi\)
\(912\) −19.0993 −0.632442
\(913\) −77.3110 −2.55862
\(914\) 1.94171 0.0642259
\(915\) 6.18724 0.204544
\(916\) 8.73606 0.288648
\(917\) 0 0
\(918\) −0.674809 −0.0222720
\(919\) −9.94808 −0.328157 −0.164078 0.986447i \(-0.552465\pi\)
−0.164078 + 0.986447i \(0.552465\pi\)
\(920\) −2.53989 −0.0837377
\(921\) −1.78236 −0.0587307
\(922\) 7.09585 0.233689
\(923\) −30.8144 −1.01427
\(924\) 0 0
\(925\) −35.9191 −1.18101
\(926\) 13.4476 0.441914
\(927\) −14.9268 −0.490259
\(928\) −0.0577297 −0.00189507
\(929\) −35.2695 −1.15715 −0.578577 0.815628i \(-0.696392\pi\)
−0.578577 + 0.815628i \(0.696392\pi\)
\(930\) 1.26475 0.0414726
\(931\) 0 0
\(932\) −28.9040 −0.946781
\(933\) 12.2745 0.401848
\(934\) −10.3874 −0.339885
\(935\) 6.01189 0.196610
\(936\) −5.03542 −0.164588
\(937\) 31.4143 1.02626 0.513131 0.858311i \(-0.328486\pi\)
0.513131 + 0.858311i \(0.328486\pi\)
\(938\) 0 0
\(939\) 3.15436 0.102939
\(940\) −6.48498 −0.211517
\(941\) 54.8731 1.78881 0.894405 0.447258i \(-0.147599\pi\)
0.894405 + 0.447258i \(0.147599\pi\)
\(942\) −7.21194 −0.234978
\(943\) 3.12066 0.101623
\(944\) 23.9349 0.779016
\(945\) 0 0
\(946\) 12.7043 0.413054
\(947\) −20.2918 −0.659396 −0.329698 0.944086i \(-0.606947\pi\)
−0.329698 + 0.944086i \(0.606947\pi\)
\(948\) 10.7311 0.348530
\(949\) 28.3905 0.921595
\(950\) −10.2503 −0.332563
\(951\) 6.09319 0.197585
\(952\) 0 0
\(953\) 7.54182 0.244303 0.122152 0.992511i \(-0.461021\pi\)
0.122152 + 0.992511i \(0.461021\pi\)
\(954\) −0.204373 −0.00661681
\(955\) 13.4406 0.434928
\(956\) −49.9170 −1.61443
\(957\) 0.0822193 0.00265777
\(958\) −8.07798 −0.260988
\(959\) 0 0
\(960\) 2.81965 0.0910037
\(961\) 5.06211 0.163294
\(962\) 10.0162 0.322934
\(963\) −7.58526 −0.244431
\(964\) −18.8650 −0.607601
\(965\) −0.270214 −0.00869849
\(966\) 0 0
\(967\) −53.0827 −1.70702 −0.853512 0.521073i \(-0.825532\pi\)
−0.853512 + 0.521073i \(0.825532\pi\)
\(968\) −31.1065 −0.999801
\(969\) −10.9228 −0.350890
\(970\) −3.59384 −0.115391
\(971\) −41.4620 −1.33058 −0.665290 0.746585i \(-0.731692\pi\)
−0.665290 + 0.746585i \(0.731692\pi\)
\(972\) 1.86448 0.0598031
\(973\) 0 0
\(974\) −7.94786 −0.254666
\(975\) 16.5389 0.529668
\(976\) −34.6645 −1.10958
\(977\) 58.5821 1.87421 0.937103 0.349053i \(-0.113497\pi\)
0.937103 + 0.349053i \(0.113497\pi\)
\(978\) −5.72809 −0.183164
\(979\) −16.2827 −0.520398
\(980\) 0 0
\(981\) −10.2791 −0.328185
\(982\) −14.1428 −0.451314
\(983\) −42.8900 −1.36798 −0.683990 0.729492i \(-0.739757\pi\)
−0.683990 + 0.729492i \(0.739757\pi\)
\(984\) 1.42265 0.0453524
\(985\) −5.97845 −0.190489
\(986\) −0.00967802 −0.000308211 0
\(987\) 0 0
\(988\) −39.3236 −1.25105
\(989\) 18.7855 0.597345
\(990\) 1.20738 0.0383732
\(991\) 11.9612 0.379960 0.189980 0.981788i \(-0.439158\pi\)
0.189980 + 0.981788i \(0.439158\pi\)
\(992\) −24.1724 −0.767473
\(993\) −30.2082 −0.958627
\(994\) 0 0
\(995\) 10.0725 0.319320
\(996\) −25.1438 −0.796711
\(997\) −16.9681 −0.537386 −0.268693 0.963226i \(-0.586592\pi\)
−0.268693 + 0.963226i \(0.586592\pi\)
\(998\) −4.37560 −0.138507
\(999\) −7.68699 −0.243206
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))